We have applied the many-body ab-initio diffusion quantum Monte Carlo (DMC) method to study Zn and ZnO crystals under pressure, and the energetics of the oxygen vacancy, zinc interstitial and hydrogen impurities in ZnO. We show that DMC is an accurat
e and practical method that can be used to characterize multiple properties of materials that are challenging for density functional theory approximations. DMC agrees with experimental measurements to within 0.3 eV, including the band-gap of ZnO, the ionization potential of O and Zn, and the atomization energy of O$_2$, ZnO dimer, and wurtzite ZnO. DMC predicts the oxygen vacancy as a deep donor with a formation energy of 5.0(2) eV under O-rich conditions and thermodynamic transition levels located between 1.8 and 2.5 eV from the valence band maximum. Our DMC results indicate that the concentration of zinc interstitial and hydrogen impurities in ZnO should be low under n-type, and Zn- and H-rich conditions because these defects have formation energies above 1.4 eV under these conditions. Comparison of DMC and hybrid functionals shows that these DFT approximations can be parameterized to yield a general correct qualitative description of ZnO. However, the formation energy of defects in ZnO evaluated with DMC and hybrid functionals can differ by more than 0.5 eV.
We have evaluated the successes and failures of the Hubbard-corrected density functional theory (DFT+U) approach to study Mg doping of LiCoO$_2$. We computed the effect of the U parameter on the energetic, geometric and electronic properties of two p
ossible doping mechanisms: (1) substitution of Mg onto a Co (or Li) site with an associated impurity state and, (2) formation of impurity-state-free complexes of substitutional Mg and point defects in LiCoO$_2$. We find that formation of impurity states results in changes on the valency of Co in LiCoO$_2$. Variation of the Co U shifts the energy of the impurity state, resulting in energetic, geometric and electronic properties that depend significantly on the specific value of U. In contrast, the properties of the impurity-state-free complexes are insensitive to U. These results identify reasons for the strong dependence on the doping properties on the chosen value of U and for the overall difficulty of achieving agreement with the experimentally known energetic and electronic properties of doped transition metal oxides such as LiCoO$_2$.
